English

Two-generator subgroups of the pure braid group

Geometric Topology 2008-12-10 v1 Group Theory

Abstract

We show that any two elements of the pure braid group either commute or generate a free group, settling a question of Luis Paris. Our proof involves the theory of 3-manifolds and the theory of group actions on trees.

Keywords

Cite

@article{arxiv.0812.1783,
  title  = {Two-generator subgroups of the pure braid group},
  author = {Christopher J Leininger and Dan Margalit},
  journal= {arXiv preprint arXiv:0812.1783},
  year   = {2008}
}

Comments

7 pages

R2 v1 2026-06-21T11:50:01.412Z